Orifice Discharge Coefficient Research Articles

Experimental Versus Theoretical Characteristics of a High-Speed Hybrid (Combination Hydrostatic and Hydrodynamic) Bearing

The high-speed test facility designed and installed at Texas A&M to study water lubricated journal bearings has been successfully used to test statically an orifice compensated five-recess-hybrid (combination hydrostatic and hydrodynamic) bearing for two radial clearance configurations. Measurements of relative-bearing position, torque, recess pressure, flow rate, and temperature were made at speeds from 10,000 to 25,000 rpm and supply pressures of 6.89 MPa (1,000 psi), 5.52 MPa (800 psi), and 4.14 MPa (600 psi). For speeds of 10,000 and 17,500 rpm, the bearing load capacity was also investigated. A pitching instability of the bearing limited the number of test cases. A 2-dimensional, bulk-flow, Navier-Stokes numerical analysis program was used for all theoretical performance predictions. Orifice discharge coefficients used in the program were calculated from measured flow and pressure data. Reynolds numbers for flow within the bearing lands due to shaft rotation and recess pressurization ranged from 6700 to 16,500. Predictions sensitivity to ±10 percent changes in the input parameters was investigated. Results showed that performance prediction sensitivities are high for changes in discharge coefficients and negligible for changes in relative roughness. The numerical predictions of relative bearing position, recess pressure, flowrate, and torque are very accurate, provided the selected orifice discharge coefficients are correct.

Determination of installation effects for a 100 mm orifice meter using a sliding vane technique

As part of the Gas Research Institute Metering Research Facility Upstream Effects programme, a sliding vane technique is used to investigate the effects of straightening vane location on orifice discharge coefficient and velocity profile in a D = 102 mm orifice meter installation. A standard ‘concentric pattern‘ 19 tube bundle straightening vane with a length to meter tube diameter ratio of 2.5 was modified so that the distance, x, from straightening vane to orifice plate could be changed rapidly without reassembling the meter tube. This paper describes sliding vane experiments made with nitrogen gas at a pressure of 724 kPa (105 psi) in 45D and 19.5D long meter tubes downstream of a single 90° elbow at a Reynolds number of 8.8 × 10 5. Results are presented for the variation of orifice discharge coefficient for β = 0.75 as a function of sliding vane location from x/D = 5 to 42.5. Complementary results are presented for the axial velocity profile distribution measured at the orifice location in vertical and horizontal planes of the 45D meter tube by hot-film anemometer at x/D values of 5, 11, 21, 39 and 42.5.

Discharge coefficients for compressible flow through small-diameter orifices and convergent nozzles

This paper presents a study of the compressible-flow behavior of light gases through small orifices and convergent nozzles with diameters ranging from 0.9 to 1.9 mm. The subsonic and critical-flow regions for 16 orifice and nozzle flow elements with the following geometries have been tested experimentally: sharp or knife-edge orifices, straight-bore orifices, rounded-entry nozzles, and elliptical-entry nozzles. Air flow was primarily studied, but data for carbon dioxide, argon, helium, and two distinct argon-helium mixtures were also collected. In addition, the upstream temperature was varied from 295 to 700 K. The data have been reduced for correlation purposes to a discharge coefficient defined as the fraction of the isentropic, adiabatic mass flow rate attained by real fluids in an actual orifice or nozzle. An error analysis shows that the reported discharge coefficients are accurate to ± 1.2% for air flow and ± 1.6% for the other gases studied. The discharge coefficient for knife-edge orifices correlates very well with a dimensionless pressure drop for the entire range of diameters, gases, pressures and temperatures studied. The discharge coefficient does not correlate with the throat Reynolds number for compressible flow through knife-edge orifices. Moreover, an analogous behavior of the discharge coefficient for larger diameters than those tested is expected for knife-edge and thin-plate orifices. Straight-bore orifices, with length-to-diameter ratios close to or slightly greater than unity, yield discharge coefficients which are approximately independent of flow rate, upstream temperature, and gas properties. These discharge coefficients are, however, highly sensitive to the length-to-diameter ratio of the straight bore. Finally, the discharge coefficients for both rounded- and elliptical-entry nozzles correlate well with a throat Reynolds number. The correlation shows that as the Reynolds number is decreased the discharge coefficient drops precipitously for Re < 20,000. For Re > 20,000 the discharge coefficient increases slowly with increasing Reynolds number. This behavior is consistent with both previous data and fluid dynamics theory for rounded- and elliptical-entry nozzles.

A new approach for estimating the orifice discharge coefficient required in the Ashford-Pierce correlation

A new method for estimating the orifice discharge coefficient required in the Ashford-Pierce subcritical two-phase flow correlation has been developed in this study. The method is a correlation of discharged coefficient versus a dimensionless function consisting of orifice diameter and fluid properties. The newly developed method is based on field-measured production data, from 47 well tests, cover broad ranges of flow rates (210–12500 B D −1), orifice sizes (12–64, 64th in.), and gas liquid ratios (344–1780, scf STB −1). Application of the new method shows an excellent agreement between measured and predicted flow rates. The modified Ashford-Pierce correlation displays both an absolute average percent error and standard deviation about 5% (based on Ashford-Pierce data) and about 16% (based on all data used) lower than the corresponding original Ashford-Pierce values.

ORIFICE DISCHARGE COEFFICIENTS FOR POWER‐LAW FLUIDS

ABSTRACTOrifice discharge coefficients for non‐Newtonian (power‐law) fluids (5, 7.5 and 10% corn starch solutions) were measured using a closed end pipe with different orifice diameters. Results indicate that orifice discharge coefficients, found to be in the range of 0 – 0.7, are a function of the orifice diameter, fluid velocity in the orifice and the fluid rheological properties (consistency coefficient and flow behavior index). They increase with the fluid velocity, tend to be constant at high velocities and decrease when the consistency coefficient of the solution is increasing. Orifice discharge coefficients are presented as a function of the generalized Reynolds number.

Discharge coefficients of circular orifices set to the bottom of circular cylinder vessels. Flow into the air nuder head lowering with time.

The discharge coefficient of a circular orifice set concentrically to the bottom of a circular cylinder vessel was studied experimentally in the flow into the air under the head lowering with the time. The discharge coefficient of orifices Cd was determined by the conventional formula and the effect of several factors (Reynolds number Re, Weber number Wr, diameter ratio D/d, thickness-diameter ratio h/d and dimensionless head H/d) to Cd was discussed. It was found that Cd decreased with an increase of Re under a constant value of Wr, Cd was almost independent of D/d and Cd increased with an increase of h/d. Besides, we tried to formulate the effect of some factors (Re, Wr and h/d) to Cd and proposed an experimental formula in the range of Re=1100-14500, Wr=100-700 and h/d=0.1-0.4.

The effect of the location of an in-line tube bundle on orifice flowmeter performance

The Gas Research Institute has sponsored many significant flow measurement studies at the National Institute of Standards and Technology. The main thrust of the 1988 research project was to determine the effect of the location of an in-line tube bundle flow conditioner on the orifice discharge coefficient. An in-line bundle was place at four locations-7, 12, 17 and 17 pipe diameters upstream of the orifice plate in a 100 mm (4 inch) orifice meter. This research has determined that if the in-line tube bundle is placed at 7 pipe diameters, the minimum distance specified in the flow measurement standards for a 0.75 beta ratio plate, as much as 1% error in the discharge coefficient occurs. At 17 pipe diameters, the discharge coefficients of all the beta ratios are statistically the same as would be determined in ‘ideal’ conditions. These new experimental data will help to improve the current flow measurement standards and suggest the direction of future reserach.

A note on the discharge coefficients of annular orifices

Discharge coefficients for annular orifices formed between pistons and a cylindrical bore are reported for twelve pistons having orifice length to gap ratios in the range 12 to 50. Square-edged, radiused and tapered orifices are examined at high fluid pressure differentials with Reynolds number varying in the range 500-4000. The radial gaps were determined by examining the flow for each piston geometry at low Reynolds numbers.

Field Calibration of Orifice Meters for Natural Gas Flow

This paper presents the orifice calibration results for nominal 15.24, 10.16, and 5.08-cm (6, 4, 2-in.) orifice meters conducted at the Chevron’s Sand Hills natural gas flow measurement facility in Crane, Texas. Over 200 test runs were collected in a field environment to study the accuracy of the orifice meters. Data were obtained at beta ratios ranging from 0.12 to 0.74 at the nominal conditions of 4576 kPa and 27°C (650 psig and 80°F) with a 0.57 specific gravity processed, pipeline quality natural gas. A bank of critical flow nozzles was used as the flow rate proving device to calibrate the orifice meters. Orifice discharge coefficients were computed with ANSI/API 2530-1985 (AGA3) and ISO 5167/ASME MFC-3M-1984 equations for every set of data points. The uncertainty of the calibration system was analyzed according to The American National Standard (ANSI/ASME MFC-2M-A1983). The 10.16 and 5.08-cm (4 and 2-in.) orifice discharge coefficients agreed with the ANSI and ISO standards within the estimated uncertainty level. However, the 15.24-cm (6-in.) meter deviated up to − 2 percent at a beta ratio of 0.74. With the orifice bore Reynolds numbers ranging from 1 to 9 million, the Sand Hills calibration data bridge the gap between the Ohio State water data at low Reynolds numbers and Chevron’s high Reynolds number test data taken at a larger test facility in Venice, Louisiana. The test results also successfully demonstrated that orifice meters can be accurately proved with critical flow nozzles under realistic field conditions.

The API/GPA Orifice-Plate Data Base

API and the Gas Processors Assoc. (GPA) have completed a four-year, $1.4 million program to develop a new archival data base for flange tapped orifice coefficients. This paper describes this project and the results to date.

Hydraulics of Perforated Terrace Inlet Risers

ABSTRACT TERRACE inlet risers perforated with circular and slot orifices were tested in the laboratory. The orifice discharge coefficient for a circular orifice in the cylindrical surface of a riser was found to be significantly larger than for a circular orifice in a flat plate. A simple theoretical equation was found to provide good estimates for riser discharge when correct values of discharge coefficient are used. Side orifices should be evenly distributed around the circumference of the riser to reduce vibration.

Results of a comparative in vitro study of Duromedics and Björk-Shiley monostrut mitral heart valve prostheses

Two different mechanical heart valves with annulus diameters 21–29 mm, (five Björk-Shiley monostrut tilting disc valves and five Duromedics bileaflet valves) have been tested in pulsatile flow in the mitral position of a mock circulation. Reflux, pressure, and orifice area have been measured while cardiac output was varied between 2 and 6 1 min −1. Insufficiency, mean orifice area, discharge coefficient, and performance and efficiency indices have been calculated. Mean values of insufficiency for the Björk-Shiley monostrut valves varied between 4.8 and 17.2% while the corresponding values for the Duromedics valves were in the range 6.1–17.3%. Mean values for orifice areas of the Björk-Shiley monostrut valves increased with the larger valve sizes from 101.1 to 210.2 mm 2; for the Duromedics valves the area range was 134.5–262.9 mm 2. Because of the larger orifice areas the values of discharge coefficient and performance index for the Duromedic valves were higher than those for the Björk-Shiley monostrut valves. As the insufficiency of the two mechanical valves was similar, and the orifice area of the bileaflet valves was greater than that of the tilting disc valves, Duromedics valves gave higher values for the efficiency index, which varied between 0.31 and 0.39; for Björk-Shiley monostrut valves the index varied between 0.24 and 0.28 under the same test conditions. This hydrodynamic in vitro comparison of mechanical heart valves showed that the Duromedics bileaflet valves were superior to the Björk-Shiley tilting disc valves.

Determination of standpipe pressure profiles and slide valve orifice discharge coefficients on synthol circulating fluidized-bed reactors

A Synthol Circulating Fluidized-Bed (CFB) reactor utilizes a finely divided, reduced iron oxide catalyst to convert (CO + H 2) to gaseous and liquid fuels. The reactor consists essentially of a fast-fluidized bed with a hopper and standpipe providing a pressure seal sufficient to maintain a high catalyst inventory in the reaction zone. For optimum reactor operation, the catalyst must flow down the standpipe in the dense-phase fluidized-flow regime so giving maximum pressure recovery. Tests carried out on the Sasol 1 commercial reactors showed that the dense-phase flow regime could be maintained with minimal use of added aeration. Work carried out on a large cold-model hopper and standpipe showed that added aeration was vital in maintaining dense-phase flow and in achieving a high pressure recovery. The relatively high pressure operation of the commercial reactors and consequent low compression effect going down the standpipe is such that the entrapped aeration entering the standpipe is sufficient to prevent a flow regime transition to a packed bed. Orifice discharge coefficients determined on the commercial reactors and the cold model agreed closely with values reported in the literature.

Rectangular Lateral Orifices in Open Channels

The theory of lateral flow through a two‐dimensional channel outlet is used to derive an expression for the flow through a rectangular lateral orifice discharging from a rectangular channel. The orifice discharge coefficient is expressed as a function of a parameter relating the length of the orifice and the width of the main channel and a parameter denoting the ratio of the mean velocity in the main channel to the resultant velocity of the jet through the orifice. Experimental results are provided to validate the proposed expressions for the orifice discharge coefficient.

Orifice Contraction Coefficient for Inviscid Incompressible Flow

The theory for steady flow of an incompressible fluid through an orifice has been semi-empirically established for only certain flow conditions. In this paper, the development of a more rigorous theory for the prediction of the orifice flow contraction effect is presented. This theory is based on the conservation of momentum and mass principles applied to global control volumes for continuum flow. The control volumes are chosen to have a particular geometric construction which is based on certain characteristics of the Navier-Stokes equations for incompressible and, in the limit, inviscid flow. The treatment is restricted to steady incompressible, single phase, single component, inviscid Newtonian flow, but the principles that are developed hold for more general conditions. The resultant equations predict the orifice contraction coefficient as a function of the upstream geometry ratio for both axisymmetric and two-dimensional flow fields. The predicted contraction coefficient values agree with experimental orifice discharge coefficient data without the need for empirical adjustment.

Cablegation: 11. Simulation and Design of the Moving-Plug Gated Pipe Irrigation System

ABSTRACT THE hydraulics of a moving-plug gated pipe irrigation system are analyzed. A relationship was developed for predicting orifice discharge coefficients for a range of typical pipe flow velocity and head conditions. A simula-tion model was developed to predict the time distribution of orifice flows, the distribution of infiltrated water across a field, and runoff rates. The model can be used to design cablegation systems for fields having variable pipe slopes and variable furrow lengths. Orifice sizes are varied along the pipe line and the plug travel speed is varied in order to obtain optimum net water application for all furrows and to keep the furrow stream sizes within acceptable limits.

Linear Fluid Resistance Using Switching Valves and a Tank

An active linear fluid resistance is demonstrated using the switched capacitor concept from electronics. For the analogous fluid component, this requires using switching valves to alternately fill and empty a tank. Analysis shows that the equivalent linear resistance is directly proportional to the switching period and inversely proportional to the tank capacitance. For fluid components, the linearity is restricted to those cases where complete filling and emptying is achieved. The time period required to insure linearity is derived in terms of fluid circuit variables. As a result, there is a lower limit on the magnitude of resistance that can be obtained for a given fluid circuit. This magnitude depends on circuit component values, as well as on the desired operating pressure range. However, the net result is that we may construct a linear fluid resistance that has no dependence on orifice sizes, discharge coefficients, or Reynolds number. The experimental fluid circuit contains a source volume in addition to the switching values and tank required for the resistance component. The source volume filters the transients and permits steady state measurements. Experiments are performed for resistances with different switching periods and tank volumes. The experimental resistance values are always within 5 percent of the theoretical predictions. The switched capacitor concept may prove useful in the design of mass flowmeters, frequency-to-analog converters, electric-to-pneumatic transducers, and temperature sensors.

Critical flowmetering: The characteristics of cylindrical nozzles with sharp upstream edges

A detailed study of the influence of axial length on the critical discharge coefficient of cylindrical orifices with sharp upstream edges is reported. Systematic consideration is given to the full range of geometries from the thin plate orifice up to the largest thickness/diameter ( t d ) ratios of practical interest. A simple theoretical approach is used together with a more complete description of the physical nature of the flow. A range of orifice geometries is identified for which the critical discharge coefficient is independent of Reynolds number and t d . Cylindrical nozzles in this range are particularly suited to critical flowmetering. They are simple to manufacture. Some new measurements are reported and these, together with existing experimental data, are shown to be consistent with the present analysis.

Effects of Swirling Flow Component on Discharge Coefficients of Constriction Meters : In Case of Orifice

Discharge coefficients of pipe orifices in swirling flow were measured and the results were discussed theoretically. Differential pressure across the orifices is affected by the swirling component and its amount is found to be a function of two parameters ; the rate of constriction of orifice opening and the intensity of swirling component. In a small orifice opening the differential pressure is decreased by the swirling component, and in a larger orifice opening it is increased. Relative change of the differential pressure was calculated theoretically by using a potential flow model. Distributions of velocities and pressures were measured and changes of energy and momentum of the flow through the orifices were discussed.

Mass spectrometric sampling of ions from atmospheric pressure flames—I: Characteristics and calibration of the sampling system

A sampling system is described for taking ions from an atmospheric pressure flame into a mass spectrometer for analysis. Several features of the formation of an ion beam are described. It is found that light ions are easier to gather into a beam than heavy ones and also that conditions can be attained where the transmission of ions through the instrument is maximised. Despite this it appears that molecular ions in particular are scattered, often in reactive collisions, in the early stages of beam formation. For the operating conditions chosen, the transmission of the apparatus appears to be quite fortuitously independent of the mass of the ion observed. The response is found to be linear, as well as independent of mass, for detected ion currents below a certain value, above which ‘beam spreading’ is important. Techniques are described for calibrating the instrument, so that absolute flame ion concentrations can be measured. For this it was necessary to determine the discharge coefficients of the sampling orifices used. Measurements have been made of the extent by which various ion beams are scattered inside the first vacuum chamber; these are found to be normally about 10%, varying from ion to ion, and also nearly independent of the flame being sampled.